Exhaustion and annihilator classification for nonzero Whittaker modules of the Witt algebra

Let $\mathfrak{w}_n$ be the Witt algebra with positive nilpotent subalgebra $\mathfrak{n}_+$, and let $L(\lambda,\mu)$ be the modules constructed in Theorem 91 from parameters satisfying the theorem's hypothesis; assume $\lambda\neq0$. Witt-algebra classification conjecture. These modules constitute an exhaustive list of simple Whittaker modules with $\lambda\neq0$ for the Whittaker pair $(\mathfrak{w}_n,\mathfrak{n}_+)$. Moreover,

$$L(\lambda,\mu)\cong L(\lambda,\mu')$$

if and only if

$$\operatorname{Ann}_{U(\mathfrak{g})}M^-(-\mu)=\operatorname{Ann}_{U(\mathfrak{g})}M^-(-\mu').$$

The conjecture would classify all nonzero-parameter simple Whittaker modules and identify their isomorphism classes through annihilators of the corresponding opposite Verma modules. The source gives no evidence of resolution.